Theoretical Study On Quantum Entanglement In One-dimensional Spin Chain System

The recent development in quantum mechanics provides new methods and principles for information science. As one of the most important applications, quantum information is a new combination of quantum mechanics and information science and has developed into a popular research field. Meanwhile, quantum entanglement is one of the most striking features of quantum mechanics and is regarded as a fundamental resource for quantum information processing. It has been widely used in quantum teleportation, superdense coding, quantum cryptographic key distribution, quantum computation and so on. So a further study on entanglement is very important for basic quantum information theory and future potential applications. On the other hand, a real quantum system will unavoidably interacts with the surrounding environment and thus leads to decoherence and disentanglement. This is a fundamental obstacle to the realization of quantum entanglement. Therefore, taking into account the effect of decoherence on entanglement dynamics is indispensable. In this thesis, based on the character of quantum state of spin chain system, the quantum entanglement and its evolution in one-dimensional spin chain system are investigated theoretically. The thesis is dived into five chapters, with our work included in chapters 2 through 5.In chapter 1, the background and basic theory of quantum information are introduced, as well as the quantum entangled state and its application are briefly described, and then the concept of quantum decoherence and one-dimensional spin chain are given at the end of this chapter.In chapter 2, the thermal entanglement in the (1/2,1) mixed-spin Heisenberg model is investigated firstly. Through comparison with the spin-half system, the (1/2,1) mixed-spin is superior in generation of thermal entanglement. And then the thermal entanglement in different Heisenberg models and quantum teleportation in the thermally entangled channel are studied. Here the effects of the intrinsic properties and external conditions of the Heisenberg model on the thermal entanglement and the teleportation fidelity are concerned. It is shown that the thermal entanglement and the quality of teleportation can be enhanced by adjusting the values of the anisotropy parameter, external magnetic field and Dzyaloshinsky-Moriya (DM) interaction.In chapter 3, the phenomenon of entanglement sudden death is studied. As to the entanglement evolution between two Tavis-Cummings atoms, the results show that the initial portion of the double excited state in the initial states is responsible for the sudden death of entanglement, and the degree of this effect also depends on the form of the initial state。In addition, the dynamic evolution of pairwise entanglement in a four-qubit Heisenberg XX spin chain is also studied. It is shown that the entanglement sudden death effect can be weakened when the periodic boundary condition and the magnetic impurity are introduced.In chapter 4, the entanglement evolution and teleportation in the different Heisenberg spin chains with intrinsic decoherence taken into account are investigated. The results show that the effects of intrinsic decoherence on the entanglement evolution and teleportation fidelity rely strongly on the initial state. Controlling the uniform or inhomogeneous magnetic fields and DM interaction can not only generate stationary entanglement, but also enhance the value of stationary entanglement. So the destructive effect of intrinsic decoherence on the entanglement evolution and teleportation can be moderated in this way.In chapter 5, the entanglement dynamics and decoherence of a three-qubit system under a quantum spin environment at a finite temperature in the thermodynamical limit are studied firstly. It is shown that the evolution of pairwise entanglement depends on the parameters related to the system and the spin environment. In addition, an undesirable entanglement sudden death occurs in the process of entanglement evolution, and this effect can be controlled by the coupling constant between two qubits, external magnetic field, and the interaction between the system and the environment. In addition, the entanglement dynamics between two central spins coupled to an XY spin chain at finite temperature with the DM interaction is also investigated. By studying the entanglement decay of the central spins, the results suggest that the DM interaction does not affect the behavior of quantum phase transition induced by the external magnetic field and does not induce new critical regions in the XY model. Moreover, the DM interaction can efficiently enhance or suppress the entanglement between the central spins which depends on the values of the DM interaction, the magnetic intensity and the temperature of the environmental spin chain.Finally, the results are summarized and suggestions for future research work are given.